Parallel implementations of the Kalman filter for tracking applications
Abstract
Parallel implementations of the extended covariance Kalman filter (ECKF) and the extended square root covariance filter (ESRCF) for tracking applications are disclosed. The use of the decoupling technique in the ECKF eliminates the need for a matrix inversion, and results in the time and measurement updates of m decoupled (n/m)dimensional state estimate error covariance P0(k)'s instead of 1 coupled ndimensional covariance matrix P(k), where m denotes the tracking dimension and n the number of state elements. Similarly, the use of the decoupling technique to the ESRCF separates the time and measurement updates of 1 coupled square root P(k) into those of m decoupled square root P0(k)'s. The updates of m decoupled matrices are found to require less computation than those of 1 coupled matrix, and they may be performed for each axis in parallel. In the parallel implementation of time and measurement updates of P(k) in the ECKF, the updates of m decoupled P0(k)'s are found to require about m times less number of processing elements and clock cycles than the updates of 1 coupled P(k)'s; an analogous phenomenon is found for parallel implementation in the ESRCF. The transformation of the Kalman gain which accounts for the decoupling of P(k) and square root P(k) is found easy to implement. The sparse nature of the measurement matrix and the sparse, band nature of the transition are explored to simplify matrix multiplications.
 Publication:

Ph.D. Thesis
 Pub Date:
 March 1990
 Bibcode:
 1990PhDT........47L
 Keywords:

 Kalman Filters;
 Radar Tracking;
 Tracking Filters;
 Tracking Problem;
 Covariance;
 Decoupling;
 Matrices (Mathematics);
 Parallel Processing (Computers);
 Systolic Arrays;
 Communications and Radar